Tailoring Enhanced Optical Chirality: Design Principles for Chiral Plasmonic Nanostructures

Martin Schaferling, Daniel Dregely, Mario Hentschel, and Harald Giessen*

4th Physics Institute, Research Center SCoPE, and Research Center SimTech, University of Stuttgart,Pfaffenwaldring 57, 70550 Stuttgart, Germany

(Received 24 August 2011; revised manuscript received 5 April 2012; published 14 August 2012)

Electromagnetic fields with strong optical chirality can be formed in the near field of chiral plasmonic

nanostructures. We calculate and visualize the degree of chirality to identify regions with relatively high

values. This analysis leads to design principles for a simple utilization of chiral fields. We investigate

planar geometries, which offer a convenient way to access the designated fields, as well as three-

dimensional nanostructures, which show a very high local optical chirality.

DOI: 10.1103/PhysRevX.2.031010 Subject Areas: Metamaterials, Optics, Plasmonics

I. INTRODUCTION

An object that cannot be superimposed onto its mirrorimage is called chiral. When chiral objects (such as mostbiological molecules) interact with circularly polarizedlight, which is chiral itself, effects like circular dichroismor optical rotatory dispersion can occur [1]. In recent years,chiral plasmonic nanostructures have gained substantialinterest [2–4]. Chiroptical effects that are several ordersof magnitude higher than those for common biomoleculeshave been reported even in planar structures [5,6]. Novelfabrication techniques also enabled the analysis of bilay-ered [7–9] and three-dimensional [10–14] chiral nano-structures. Such structures exhibit not only a high amountof circular dichroism and optical rotatory dispersion, butthey can also massively enhance the signals obtained frombiological molecules [15–18], which in principle providesa method to detect, with a very high sensitivity, the handed-ness of a given molecule.

To quantify this enhancement, the so-called optical chi-rality C, which is a time-even pseudoscalar, can be used[19–21]:

Cð ~rÞ ¼ 1

2

�"0 ~Eð ~rÞ � ~r� ~Eð ~rÞ þ 1

�0

~Bð ~rÞ � ~r� ~Bð ~rÞ�; (1)

where ~E and ~B are the electric and magnetic fields, respec-tively. In the first discussion of this value in 1964, onlymathematical aspects were analyzed. No physical meaningwas assigned to that quantity [19]. Nevertheless, it hasrecently been shown that the optical chirality is correlatedto the rate of excitation A of a chiral molecule [22]:

A / �!Ue � �C; (2)

where ! and Ue are the angular frequency and the localelectric energy density of the surrounding field, respec-tively. � and � denote material parameters describing themolecule [23]. The parameter� is of special importance asit is of opposite sign for the two enantiomers of a handedmolecule [24]. The difference in A therefore depends onthe optical chirality C of the incident light. If one canincrease this property at the location of the chiral molecule,the sensitivity for the detection of the handedness of themolecule can be enhanced.We show that plasmonic nanostructures are suitable for

this enhancement. While this has already been demon-strated in principle [15], we perform the first systematiccomparison between different plasmonic nanostructuresthat leads the way to tailor such structures for specificapplications such as enantiomeric sensing. Appropriatedesigns should provide not only a high enhancement ofthe optical chirality, but also large continuous regionswhere the fields with enhanced chirality are located andcan be accessed, for example, by chiral liquids or mole-cules. We here work out several design principles that helpto fulfill these requirements.

II. RESULTS AND DISCUSSION

To calculate the optical chirality, a simpler version ofEq. (1) can be deduced [22]:

Cð~rÞ ¼ � "0!

2Im

�~E�ð ~rÞ � ~Bð ~rÞ

�: (3)

Note that ~E and ~B here denote the complex field ampli-tudes. We calculate the local enhancement of the opticalchirality as

Cð ~rÞ� :¼ C�

jC�CPLj

(4)

for left-handed (LCP, þ) and right-handed (RCP, �) cir-cularly polarized light as incident waves. C�

CPL are the

values obtained for circularly polarized light without thenanostructure [25]. The sign of C is preserved during thisnormalization, which helps to distinguish regions with

*giessen@physik.uni-stuttgart.de

Published by the American Physical Society under the terms ofthe Creative Commons Attribution 3.0 License. Further distri-bution of this work must maintain attribution to the author(s) andthe published article’s title, journal citation, and DOI.

PHYSICAL REVIEW X 2, 031010 (2012)

2160-3308=12=2(3)=031010(9) 031010-1 Published by the American Physical Society

different handedness of the local field. Afterward, wevisualize the chiral fields via three-dimensional volumeplots. Hereby, different nanostructures can be comparedby the shape and the distribution of the regions withenhanced optical chirality. We use the same range for thecolor schemes in all plots, which allows for a directcomparison of different structures. Additionally, a roughcomparison is possible by analyzing the minimum andmaximum values gained for each structure. We use amedian filter to smoothen the simulated data from numeri-cal noise, which occurs in the form of single points withunnaturally high chirality values [26].

A. Plasmonic structures for enantiomeric sensing

First, we will discuss the general applicability of plas-monic nanostructures for enantiomeric sensing. By now,the most common method to detect the handedness ofchiral molecules is a circular dichroism measurement.With this method, one illuminates the sample with left-and right-handed circularly polarized light and detects thedifference signal of transmission or absorption [27]. In amore general scheme, one could use just two different lightfields. For such measurements, the enantioselectivity isquantified by the dissymmetry factor g, which is defined as

g :¼ 2ðAþ � A�ÞAþ þ A� : (5)

If the two light fields differ only in the sign of their localoptical chirality, the dissymmetry factor is proportional to�C=Ue

[22]. This is, of course, the case for circularly

polarized light. However, it has been demonstrated re-cently that the enantioselectivity can be enhanced using apartially reflecting mirror. The electric-field density islowered at some spatial positions due to interference, whilethe optical chirality remains independent of position. Thiseffect has been referred to as superchiral light as thedissymmetry factor exceeds the one obtained for circularlypolarized light [20]. However, the relation between thetotal energy density of the field and the optical chiralityremains independent of position, because, for regions withlow electric energy density, the magnetic-energy density isincreased [28]. Nevertheless, the excitation due to an ex-ternal magnetic field is negligibly small and thereforeirrelevant for enantiomeric sensing [22].

However, when we look at plasmonic nanostructuresinstead of the above-mentioned interference of planewaves, our analysis reveals that—depending on the polar-ization state of the incident light—different chiral fieldscan be induced. In general, the local optical chirality differsnot only in sign but also in magnitude near the nanostruc-ture. Additionally, the electric energy density can changewhen the incident polarizations excite different plasmonicmodes. Of course, one could calculate the dissymmetryfactor using Eq. (5). But using this formula would restrictthe calculation to one specific chiral molecule, as the

material constants � and � have to be taken into accountto obtain A�.To obtain some general insight despite that issue, we

analyze a superstructure composed of both of the enan-tiomers of one given chiral plasmonic structure (cf. Fig. 1).When one changes the polarization of the incident light,the optical chirality exhibits no local sign flips. Rather, foreach spatial location near one enantiomer, there exists acorresponding location near the other where the fieldsfeature the same electric energy density and opposite opti-cal chirality. Then, the dissymmetry factor for two mole-cules located at these positions (which we refer to as g�)becomes [29]

g� / � Cþ � C�

Uþe þU�

e

: (6)

Note that only one of the enantiomers of the structure isactually involved in this calculation. We use the left-handed enantiomer as it normally shows the stronger re-sponse to incident left-handed circularly polarized light.In the following discussion, we carry out this kind of

analysis for a helical structure, being one of the mostintuitive examples for a chiral plasmonic nanostructure.Indeed, it has been demonstrated that such a structure ex-hibits very strong circular dichroism [30]. We used a goldhelix with twowindings, a diameter as well as a total heightof 400 nm, and a wire thickness of 80 nm. This structure isresonant to incident light at a wavelength of 2:03 �mwhenthe handedness of the incident polarization matches the oneof the helix. Therefore, one can expect a strong difference inresponse for the two circular polarization states.Figure 2 depicts the calculated optical chirality for such

helices. We show only the cases with matching incidentpolarization because, for the nonmatching configurations,the absolute values of optical chirality are too small to bevisible in the three-dimensional map. The two enantiomers

FIG. 1. To calculate the enantioselectivity in presence of chiralplasmonic structures, a modified dissymmetry factor g� is used.The definition requires a superstructure composed of both of theenantiomers of the single chiral nanostructure. Chiral probemolecules of one handedness (sketched as red spheres) areplaced at corresponding positions at each of the enantiomerswhere the near fields differ only in the sign of optical chiralitywhen the incident polarization is switched.

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of the helix show symmetric distributions of enhancedoptical chirality with respect to each other. More precisely,the values of optical chirality feature the same magnitudebut opposite sign at corresponding positions. Therefore,the dissymmetry factor g� [cf. Eq. (6)] can be calculated.

The result is shown in Fig. 3(a) where we plot theenhancement g� of g� with respect to the value g obtainedfor circularly polarized light. This is carried out in the same

way as the calculation of C [cf. Eq. (4)]. Note that thisfactor is not for the single helix, but rather for a combina-tion of both the left-handed and the right-handed helices asdepicted in Fig. 1. For a real application, one has to coversymmetric regions of both of these structures with thechiral sample.

We find a quite complicated distribution of g� that is

different from the one for C plotted in Fig. 2. This is due to

the contribution of the electric energy density to the dis-symmetry factor which is also high at locations with strongoptical chirality [cf. Fig. 3(b)]. As the electric-field en-hancement is much stronger than optical chirality enhance-ment, the dissymmetry factor is in the end lower than forcircularly polarized light at these positions. However, thecalculation shows that there are regions where also thedissymmetry factor and therefore the enantioselectivity isincreased. We have reached an enhancement factor of up to7 for this model configuration. Note that the superstructureused for this analysis is achiral as it consists of both ofthe enantiomers of the chiral plasmonic helix. Therefore,we expect no chiroptical far-field response in the absenceof chiral molecules, which allows for background-freemeasurements.Of course, this is not a useful configuration for real

sensing applications. Not only is the enhancement toosmall, but also the fabrication of the chosen structure ischallenging due to the three-dimensional shape and thesmall dimensions. Also, the regions with enhanced enan-tioselectivity would be difficult to access. Yet, this exampleshows that chiral plasmonic nanostructures can indeedenhance the sensitivity of an enantiomer sensor.In the following discussion, we will investigate different

structures that overcome these problems. To keep to thegeneral aim of this work, we decided to restrict our furtheranalysis to the enhancement of optical chirality and leavethe calculation of the dissymmetry factor to future work.Our results can be directly used for a simpler detectionscheme in which the rate of excitation for just one incidentpolarization is measured directly. This scheme also allowsfor a distinction between the two enantiomers of thatmolecule due to the change of the sign of � in Eq. (2).Our analysis of optical chirality enhancement will alsosuit other imaginable applications based on this quantity.As a consequence of the general approach, it is up to thereaders to adopt our results to the needs of their specificapplications.

B. Planar nanostructures

We start with an analysis of optical chirality enhance-ment by the gold gammadion structure introduced inRef. [15] with respect to enantiomeric sensing. We usesimilar dimensions: 80 nm for both the width of the armsand the gaps, leading to a total width of 400 nm, but a goldthickness of 20 nm instead of 100 nm. For different sizes ofthe nanostructure, we expect the optical chirality to scalewith the electric dipole moment of the particle plasmon,and hence with the volume of the individual nanoparticles.The structure is embedded in air. We calculate the fields atthe fundamental plasmon resonance at 2:01 �m.In contrast to the helix, the gammadion shows a similar

behavior for both LCP and RCP as incident polarizations(cf. Fig. 4). We calculate enhancement factors for opticalchirality in the range of 20, which is comparable to the

FIG. 2. Optical chirality enhancement for (a) a left-handedhelix with left-handed circularly polarized light and (b) aright-handed helix with right-handed circularly polarized lightat a wavelength of 2:03 �m. Diameter and height of the helix are400 nm with a gold thickness of 80 nm. Both combinations showenhanced optical chirality where the values of maximum andminimum enhancement are denoted by the black horizontal linesacross the color bars. The regions with enhanced optical chiralityare located at corresponding positions of the respective helix, buttheir signs flip. The pictures addressing the polarization state aretaken from the detector’s view; hence, the direction of the arrowindicates the handedness of the field vectors in space at a fixedtime.

FIG. 3. (a) Enhancement of dissymmetry factor g� near aplasmonic helix structure with respect to circularly polarizedlight. Superchiral light fields with up to 7 times higher enantio-selectivity could be obtained. This value does not follow theenhancement of optical chirality directly, as (b) the enhancementof electric energy density Ue also enters the calculation. Theelectric energy density shows similar distributions as opticalchirality, leading to more complicated shapes of the superchirallight fields. Note the different scale of the color bar related to theplot of g� compared to the plots of C in Fig. 2.

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values obtained for the helix. As a major difference, thegammadion shows both positive and negative values ofoptical chirality with similar absolute values, while forthe helix the values corresponding to light with matchingpolarization are higher [31].

The regions with locally enhanced optical chirality aremainly located at the front and the back of the four arms. Incontrast, the regions with highest field enhancement can befound at the end of each arm and in the gaps beneath theseends (cf. Fig. 5). This result shows that such a nanostruc-ture focuses the optical chirality at distinct points in space,similar to the field-enhancement effect. Nevertheless, theregions with highest enhancements differ for the two quan-tities. High field enhancement is therefore not sufficient toobtain a strong optical chirality as the polarization of theincident light is not maintained by the field-enhancementeffect.

A drawback of the gammadion design is that regionswith enhanced optical chirality are at the same position andhave the same sign for both incident polarizations; only theabsolute values differ. Therefore, a change of the incidentpolarization will result in only a small change of the opticalchirality at a certain position, which renders this design

impractical for any application using more than one lightdistribution. As additional disadvantages, the enhancementis discontinuous and overall quite small.In Fig. 6 we show a more advanced planar nanostructure,

namely, the nanospiral. Compared to the gammadion, thespiral features fewer sharp corners, which allows forsmoother distributions of the regions with enhanced opticalchirality. The two-armed design is chosen to operate at1:84 �m [32] with comparable dimensions (80 nm as thearm width with a gold thickness of 20 nm). Each spiralfeatures one and a half rotations, while the gammadionoffers only one 90� kink at each arm.As a result, the two incident polarizations show different

behavior, which can be explained by Fig. 7 where theinduced current distributions for incident LCP and RCPlight are plotted. The different polarizations excite differ-ent modes. Left-handed circularly polarized light excitescurrents in the outer part of the structure, which leads to theringlike region with enhanced chirality, while the enhancedregion for right-handed circularly polarized light is con-centrated more in the center. Also, the signs of the chiralityat the front and the back of the spiral along the z directionchange for the different polarizations.This sign flip leads to a significant advantage over the

gammadion: When one changes the polarization state ofthe incident light, the optical chirality changes in amuch stronger fashion. This strong change aids anyapplication that makes use of two different incidentpolarizations and analyzes a quantity influenced by thedifference of optical chirality.The plot of the difference in optical chirality enhance-

ment �C ¼ Cþ � C� shows quite uniform shapes[cf. Fig. 8(a)]. The regions with different polarity areclearly divided by the structure itself. For many applica-tions such as enantiomer sensing or vibrational and rota-tional optical activity measurements, one wants to use onlyone particular polarity, as the second polarity would possi-bly lessen the signal. This use of a particular polarity can besimply accomplished for the nanospiral, as one has only toensure that the access is limited to one side of the structure.When the structure is fabricated on top of a substrate, thisrequirement is automatically fulfilled [cf. Fig. 8(b)].

FIG. 4. Optical chirality enhancement by a planar gammadion structure illuminated with (a) LCP and (b) RCP at a wavelength of2:01 �m. The structure exhibits similar shapes for the regions with enhanced chirality for both polarizations; only the values differ (asbest seen in the two-dimensional slice views).

FIG. 5. Enhancement of the electric energy density Ue by theplanar gammadion structure illuminated with right-handed cir-cularly polarized light at a wavelength of 2:01 �m. As for theoptical chirality, the electric energy density has been normalizedby the value obtained for RCP without the presence of thenanostructure. Strongest enhancement can be found at the endof each arm and the nearby gaps. For LCP, the enhancement issimilar in shape.

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It is important to note that all structures analyzed thus farare achiral, as planar structures cannot possess structuralchirality in a three-dimensional space. Nevertheless, thecomparison between gammadion and nanospiral showsthat stronger optical chirality as well as a more uniformenhancement can be obtained by a structure with a strongertwist. This twist can be referred to as planar chirality.Although the chiral far-field response of such structuresoccurs only in the presence of a substrate [5], the chiralnear-field enhancement is possible even without the sub-strate, as shown in our simulations.

A drawback of structures with only planar chiralityarises when the response for the two different incidentpolarizations is compared. Although the absolute values of

C are up to 50% higher than those of the gammadion, at thespatial points where the chirality enhancement for LCP isstrong, the contribution of RCP is negligibly small, and viceversa. This correlation limits the benefit of switching be-tween the two polarizations. To overcome this limitation,

one can use three-dimensional structures, which can exhibitintrinsic structural chirality.

C. Three-dimensional chiral nanostructures

The helix discussed in Sec. II A provides the desiredfeatures in principle. Although the response for any com-bination of helix and incident light with opposite handed-ness is very small, the strongest enhancement can be foundat spatial locations similar to those for the matching polar-ization but with different sign. But, as already discussed,such a structure would be impractical for real applicationsbecause of the small and discontinuous response as well asfabrication difficulties.To overcome these problems, we propose a much sim-

pler bilayered structure which mimics a helix. We call thisstructure a chiral oligomer [33–37]. The design is sketchedin Fig. 9: Each layer consists of three gold disks which are

FIG. 6. Optical chirality enhancement by a two-armed gold nanospiral with (a) LCP and (b) RCP as incident polarizations at awavelength of 1:84 �m. The two polarizations differ significantly in their near-field response. The smaller pictures on the bottom of(a) and (b) show the scenario from different angles. The enhancement of the optical chirality for the nanospiral is up to 50% higherthan for the gammadion, which can be understood by the fact that the spiral is bent everywhere.

FIG. 7. Current distributions inside the nanospiral for incident(a) LCP and (b) RCP light at wavelength 1:84 �m. The twopolarizations excite different modes. The current distributionscorrespond to the regions with enhanced optical chirality asidentified in Fig. 6.

FIG. 8. Difference �C ¼ Cþ � C� of the chirality enhance-ment of the nanospiral. (a) The side view shows that thedistribution of the enhanced regions is continuous, while thestructure separates the parts with different signs. (b) Inthe presence of a substrate, the access is automatically limitedto one polarity. Note that this picture is only a sketch, as thecalculation was performed without the substrate.

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arranged in an L-shaped configuration. The second layeris twisted by 90� to emulate the chiral layout of a helix.The stacking of several layers with planar structures isa well-established technique in nanofabrication [38].Additionally, the usage of small disks as building blocksallows for tuning of the operation wavelength to lower

values: The resonant operating wavelength is governedby the particle plasmon resonance of the individual goldnanodisks, modified by plasmon hybridization due tostrong near-field coupling [39,40]. This effect is demon-strated by the dimensions chosen in Fig. 9, which lead to astructure with maximum circular dichroism in the nearinfrared at 900 nm.Figure 10 shows the optical chirality enhancement in-

duced by the chiral oligomer. Like in the case of the helix,we obtain a much stronger result when the handednessof both the structure and the incident light coincide.

Compared to the gammadion, the response of C is about5 times higher for LCP [Fig. 10(a)], while, for incident RCP[Fig. 10(b)], still comparable values occur. The highestabsolute values for both polarizations are located at the

same spatial positions, which leads to regions with �C ofmore than 100 [Fig. 10(c)]. The analysis of the distributionof the regions with enhanced chirality reveals that (besidessome small areas near the surfaces of the disks) a continuousregion with consistent polarity is located around the twodisks at the bottom left of the oligomer. Figures 10(d)–10(f)show slices through the point with highest chirality enhance-ment (located in the gap between the top and the bottom leftdisk of the front layer). We consider that this strong effect isdue to near-field enhancement, which is highest in the small

FIG. 9. Sketch of the chiral plasmonic oligomer. The arrange-ment of the gold disks mimics the chiral structure of a left-handed helix.

FIG. 10. Optical chirality enhancement of the chiral oligomer for incident (a),(d) LCP and (b),(e) RCP light at a wavelength of900 nm. The spatial points with strongest enhancement can be found on similar spatial locations but exhibit different signs, which leadsto (c),(f) a very strong difference �C. (d)–(f) Slices through the point between the top and bottom left disk of the front layer show thatthe region with strongest enhancement is located in the gap between these two disks.

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gaps between the disks. Unfortunately, access to thesestrongly enhanced chiral fields is more challenging than inthe planar case, since the structure has to be embedded in adielectric matrix.

The third dimension offers many more possibilities forchiral structures than the two-dimensional case. In Fig. 11we obtain the optical chirality for stacked and twistedplasmonic split-ring resonators. The chiral far-field re-sponse of these so-called stereometamaterials [41] is wellknown [42,43]. The dimensions were chosen to fit thegeometry introduced in Ref. [41], which leads to a wave-length with highest circular dichroism of 1:34 �m.Interestingly, we find that, for this left-handed structure,the strongest chirality enhancement is obtained not forLCP [Fig. 11(a)], but for RCP incident light [Fig. 11(b)].For both polarizations, positive chirality values areobtained in the gap while negative values occur in thesurrounding medium. The strength of the enhancement isbetween the values of the planar structures and the chiraloligomer. The strongest enhancement is not located in thegap of one split-ring resonator but in the layer between thetwo resonators. Additional degrees of freedom such asthe twist angle could be used to tune this behavior.

III. CONCLUSIONS

We have explored the chiroptical near-field response ofdifferent planar as well as three-dimensional plasmonicnanostructures and compared the resulting enhancement

of optical chirality. Using the example of the helix, we haveshown in principle that plasmonic nanostructures can beutilized to enhance the enantioselectivity locally.When comparing different structures, there is a huge

parameter space to explore, and the optical chirality en-hancement is nontrivial to predict. Therefore, we give as aconclusion some design principles that we extracted fromour present analysis to match the demands of differentapplications. If simple access to a continuous region ofenhanced optical chirality is needed, a planar structure witha strong twist and ideally without sharp corners should beused. A versatile example for such a design is our plas-monic nanospiral. To obtain large differences of the opticalchirality, we recommend three-dimensional chiral structuresthat should be as compact as possible. The chiral oligomer,which is of that type, showed the highest chirality enhance-ment we could obtain theoretically. For easier fabrication,multilayered structures should be preferred.We have also demonstrated that local optical chirality is

a new way to look at chiral structures. A strong chiralresponse in the far field—the strongest circular dichroismfrom our selected structures could be obtained for thehelix—will not automatically generate fields with thestrongest local optical chirality. Moreover, even achiralstructures can lead to fields with high optical chirality.We found that near-field enhancement and twisting shouldbe combined, although the highest optical chirality will notautomatically occur at regions with highest electric energydensity. To understand this, additional research is needed to

FIG. 11. Optical chirality enhancement induced by the stereometamaterial with (a) LCP and (b) RCP as incident polarizations atwavelength 1:34 �m. Note that the enhancement is strongest when the handedness of the light is opposite to the handedness of thestructure. The strongest enhancement can be observed in the middle of the layer between the two split-ring resonators.

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work out the origin of the enhancement of the opticalchirality for the different structures. This future work willalso help to improve our design principles and thus tofurther optimize the suggested designs or to create newdesigns for enhanced chiral interaction [44] and enantio-meric sensing techniques.

ACKNOWLEDGMENTS

The authors thank Adam Cohen and Thomas Weiss forhelpful discussions and Sven Hein for help with the visual-ization. This work was financially supported by BMBF(Nos. 13N9048 and 13N10146), DFG (Nos. SPP1391,FOR557, and GI 269/11-1), and Baden-WurttembergStiftung. D.D. additionally acknowledges support by theCarl-Zeiss-Stiftung. This work was supported by theGerman Research Foundation (DFG) within the fundingprogram Open Access Publishing.

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